The global transition from internal combustion engines (ICEs) to hybrid (HEVs) and electric vehicles (EVs) is fundamentally reshaping lubricant design requirements, driven by evolving thermal demands, electrical constraints, and material compatibility challenges. Conventional ICE lubricants are primarily formulated to withstand high operating temperatures, mechanical stresses, and combustion-derived contaminants through established additive chemistries such as zinc dialkyldithiophosphate (ZDDP), with thermal stability and wear protection as dominant considerations. In contrast, HEV lubricants must accommodate frequent start–stop operation, pronounced thermal cycling, and fuel dilution while maintaining performance across coupled mechanical and electrical subsystems. EV lubricants represent a paradigm shift, where requirements extend beyond tribological protection to include electrical insulation and conductivity control, thermal management of electric motors and battery systems, and compatibility with copper windings, polymers, elastomers, and advanced coatings, alongside mitigation of noise, vibration, and harshness (NVH). This review critically examines lubricant behavior, formulation strategies, and performance requirements across ICE, HEV, and EV powertrains, with specific emphasis on heat transfer, electrical performance, and lubricant–material interactions, covering mineral, synthetic, and bio-based fluids. Additionally, regulatory drivers, sustainability considerations, and emerging innovations such as nano-additives, multifunctional and smart lubricants, and AI-assisted formulation are discussed. By integrating recent research into industrial practice, this work highlights the increasingly interdisciplinary role of tribology in enabling efficient, durable, and sustainable mobility for next-generation automotive systems.